Abstract
Game theory is the mathematical study of strategic interaction among rational agents and has found many applications in economics, politics, logic, AI, and computer science. Because of pervasive uncertainty in game-playing environments, how to deal with uncertainty is also a key issue in game theory. While probability calculus has been the standard theory for uncertainty management in games, information of exact probability assessment may be not available in many realistic situations. In such cases, possibility theory is an alternative tool for modeling uncertainty in games. In past decades, the cross-fertilization between logic and game theory has proved to be very successful. Therefore, the paper is aimed at the integration of possibilistic uncertainty into modal logics for reasoning about games including game logic and coalition logic. We will study syntax and semantics of the integrated logics as well as their reasoning problems.
Supported by NSTC of Taiwan under Grant No. 110-2221-E-001-022-MY3.
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Notes
- 1.
See [9] for the axiomatization of the basic many-valued logic BL.
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Liau, CJ. (2023). Reasoning About Games with Possibilistic Uncertainty. In: Huynh, VN., Le, B., Honda, K., Inuiguchi, M., Kohda, Y. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2023. Lecture Notes in Computer Science(), vol 14375. Springer, Cham. https://doi.org/10.1007/978-3-031-46775-2_5
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